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Two mathematical models of synchronization
Sang Woo Ryoo
Sang Woo Ryoo, Mathematics Department, Princeton University
Title: Two mathematical models of synchronization
Abstract: The Winfree and Kuramoto models are nonlinear ordinary differential equations describing populations of coupled oscillators that serve as mathematical models of synchronous behavior. When the intrinsic frequencies of the oscillators are identical, the dynamics are reduced by the Watanabe--Strogatz transform to actions of the M\"obius group on the unit circle and are thus extremely degenerate. On the other hand, when the intrinsic frequencies are not identical, not much is known about the long-term dynamics for generic initial data, although numerical simulations suggest they converge toward special solutions which are well-understood. I will present an approach based on the order parameter which rigorously partially describes the long-term dynamics for generic initial data. Based on joint works with Ha, Kim, Ko, and Park.
Sang Woo Ryoo, Mathematics Department, Princeton University